Computing the eigenvalues of symmetric tridiagonal matrices via a Cayley transformation

zbMath1392.65084MaRDI QIDQ1744301

David S. Watkins, Thomas Mach, Raf Vandebril, Jared Lee Aurentz

Publication date: 23 April 2018

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://etna.mcs.kent.edu/volumes/2011-2020/vol46/abstract.php?vol=46&pages=447-459

zbMATH Keywords

rotationseigenvaluesymmetric matrixcore transformationsunitary QR

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17) Orthogonal matrices (15B10)

Related Items (1)

Connecting optimization with spectral analysis of tri-diagonal matrices

Uses Software

• LAPACK
• eiscor
• GitHub

Cites Work

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• Fast and stable unitary QR algorithm
• The QR algorithm for unitary Hessenberg matrices
• A unitary Hessenberg \(QR\)-based algorithm via semiseparable matrices
• The QR Transformation A Unitary Analogue to the LR Transformation--Part 1
• LAPACK Users' Guide
• Perturbation Bounds for the $QR$ Factorization of a Matrix
• Accuracy and Stability of Numerical Algorithms

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